I've used BD gear for years and its generally good stuff - particularly at REI sale prices.
Not a bad idea to have such safety equipment if you plan to venture into areas where the snow is steeper or slicker and there aren't solid tracks/steps to follow. But, as others have already suggested, get some training first - just having more technology doesn't automatically equate to more safety.
Crampons aren't hard to use with two caveats: (1) make sure they fit your boots and (depending on what boot you're using) will stay on as the boot flexes, (2) practice walking in them so that you learn not to hook your pant leg with the side spike and flip yourself head-over-heels (and probably off down the slope), and (3) NEVER glissade with crampons on - you'll instinctively try to stop by digging in your heels which will likely cause you to flip and may even break your leg (I saw this happen once in the Sierras).
A true self-arrest on hard snow or ice with an ice axe is a learned skill - you need to be able to arrest right away, before you build-up too much speed. Once you get going, the ice axe tip will either skate or could snag, with the axe then getting ripped out of your hands. Consider learning the self-belay - where you practice stopping the slide before it even starts.